这种问题方法多样,最重要的是寻找规律.由1/(n*(n+1))=1/n-1/(n+1),根据拆项法可得1/(1*2)+1/(2*3)+1/(3*4)+.+1/(98+99)+1...1/(1*2)+1/(2*3)+1/(3*4)+.+1/(98*99)+1/(99*1000=1-1/2+1/2-1/3+...+1/99-1/100=1-1/100=...